The role of dominance in sibling relationships: differences in interactive cooperative and competitive behavior

Siblings strongly influence each other in their social development and are a major source of support and conflict. Yet, studies are mostly observational, and little is known about how adult sibling relationships influence social behavior. Previous tasks exploring dynamically adjusting social interactions have limitations in the level of interactivity and naturalism of the interaction. To address these limitations, we created a cooperative tetris puzzle-solving task and an interactive version of the chicken game task. We validated these two tasks to study cooperative and competitive behavior in real-time interactions (N = 56). Based on a dominance questionnaire (DoPL), sibling pairs were clustered into pairs that were both low in dominance (n = 7), both high in dominance (n = 8), or one low and one high in dominance (n = 13). Consistent with our hypothesis, there were significantly more mutual defections, less use of turn-taking strategies, and a non-significant trend for reduced success in solving tetris puzzles together among high dominance pairs compared to both other pair types. High dominant pairs also had higher Machiavellian and hypercompetitiveness traits and more apathetic sibling relationships. Both tasks constitute powerful and reliable tools to study personality and relationship influences on real and natural social interactions by demonstrating the different cooperative and competitive dynamics between siblings.

i. Dominant individuals would show higher motivation to win and report the use of more dominant and aggressive strategies during the game, while subordinate/cooperative individuals will report the use of fairness and turn-taking strategies.
j. Brothers would show more dominant behavior (more crashes) than sisters, who will show more cooperative behavior (turn-taking strategy).

Supplementary Methods 2.Programs and Set-up
A virtual server handled any communication for the experimental paradigm platforms using the socket module in Python 3.6.6. All tasks were synchronized by having the paradigm-presenting computers located at the respective rooms (hereafter referred to as "clients") communicating with this server over TCP/IP. These clients sent paradigm-relevant information like "readiness" and trial information to the server. Upon receiving specific messages from both clients, the server replied to both clients with an appropriate message. When both clients were connected to the server, the experimenter manually started the Cooperative Tetris Task for both clients at the same time, sending a message to Psychopy through the server. For the Interactive Chicken Game, once both clients were connected to the server, the latter automatically started the task.
In both tasks, the server waited for the confirmation of each client to ensure that both computers were synchronized with a maximum latency of approximately 16 milliseconds at the beginning of each trial.

General Criteria
A set of criteria was determined before creating the new Tetris blocks intended for use in the CoTT. Tetris blocks were structured as follows: 1. Each block would start with uniquely preassembled base pieces.
2. In every block, four Tetris pieces would need to be placed among the base pieces. Each Tetris piece represents one trial.
3. Two types of blocks were defined: a) Easy blocks (Fig. S1):  Every Tetris piece placed must be able to complete a line if the correct position and rotation are chosen (optimal position).
 Every Tetris piece placed must have one unambiguous optimal position to fit into and only choosing this option completes a line.
b) Complex blocks (Fig. S2): The complex blocks are formed by two different type of trials:  Two-option (complex) trials: The first trial must have exactly two unambiguous equally optimal positions to fit into but that does not delete a line. Optimal positions are defined as empty spaces in which if a piece is placed that fits in that spot, there is only one space left for the next piece to complete the line. If the players use the pieces as planned, the third trial again offers two equally optimal positions by which no line can be completely filled.
 One-option (easy) trials: The second and the fourth Tetris piece must have the potential to complete a line (given that the optimal position was used in the trial before). They must have an unambiguous optimal position to fit into and there can only be one option that can complete a line.
Note, that players could still place the Tetris pieces in positions not further described here although we tried to make it as obvious as possible to the players which position(s) is optimal for success. A piece that is positioned less optimal and/or the following pieces might not have the potential to clear lines as intended. ideal positions (Two-option trials) and even trials one (One-option trials). In each Twooption trial the chosen ideal location of the piece determines the ideal location of the next piece, thus resulting in two trial variants for the following One-option trial (depicted by split arrows).

Materials and Procedure
We created a total of 22 easy blocks and 22 complex blocks. We conducted a pilot study in which we presented the trials of these 44 blocks to 16 independent participants (8 males, 8 females, age range from 20 to 35 years) and asked them to indicate their first, second, and third choice of positions (later described as "field preference") in which they would place the predefined Tetris piece. For each of these three choices, they were asked to rate the likelihood of choosing this position. They were also asked whether they think that there are more than three possible positions for the piece. Additionally, participants evaluated the level of difficulty of the block (Fig. S3).
Each easy block and each complex block were composed of four trials. This made a total of 88 easy trials across all easy blocks. Since complex blocks are presented in different variations ( Fig. S2) the complex blocks contained easy (one optimal option) and complex (two optimal options) trials. Thus, there were three Two-option trials (trial 1, trial 3A, trial 3B) and six One-option trials (trial 2A, trial 2B, trial 4A, trial 4B, trial 4C, trial 4D), adding up to a total of 198 to-be-evaluated trials. Four of these trials (two Two-option trials, and two One-option trials) were deleted because we retrospectively realized that they were duplicates of other trials in the same block and seven of the complex blocks were an inverted version of another complex block. Summing up, a total of 65 complex trials and 217 easy trials for a total of 44 blocks were evaluated in the pilot study. Participants received an Excel file with all the trials to evaluate. We alternated the easy and complex blocks so that all evaluations started with four easy blocks and were followed by four complex blocks etc., in the same order for all participants.

Evaluation Analyses
We compared the difficulty between easy and complex blocks and the tendency for one or two fields. The difference in difficulty between easy and complex blocks was Selection Complex Blocks. The final 12 complex blocks were selected by the highest scores in difficulty and by the tendency for field options. The following assumptions about the Two-option trials guided our analyses: 1) The difference in the strength of participants' tendency towards the position indicated in field 1 (first position option) and their tendency towards the position indicated in field 2 (second position option) was expected to be small because the Two-option trials were designed in such a way that they would suggest two equally advantageous positions for achieving success (filling and clearing a line).
2) The difference in the strength of participants' tendency towards the position indicated in field 2 and their tendency towards the position indicated in field 3 was expected to be greater than the difference between field 1 and field 2 because the Two-option trials were designed in such a way that they would suggest only two advantageous positions for achieving success (filling and clearing a line) and not more.
Based on these considerations, we selected the 12 complex blocks calculating complex trials within complex blocks (the three Two-Option trials) that have the lowest difference between fields 1 and 2 and the greatest difference between fields 2 and 3. To take both criteria into account at the same time, we subtracted the difference between fields 1 and 2 from the difference between fields 2 and 3 and chose the blocks with a lower difference (meaning that they have a small difference between 2 and 3 and a great difference between 1 and 2).
Using a one-way ANOVA, we again compared the mean difficulty between the easy and complex blocks of the finally selected blocks. We also tested if there was a significant difference between the first preferred and the second preferred option in the complex trials, assuming that there would be no significant difference.  Table S1. Interactions between difficulty and gender, as well as field tendency and gender, were not significant.

Measures description
During the tasks, several outcome measures assessing performance and interaction were collected (see Table S3). Both crash: trial in which none of the participants decided to turn.

Mutual cooperationboth turn (TT)
Both turn: trial in which both participants turned in the same interval, losing the same number of points.

One-turning (TD, DT)
One dominant, one subordinate: trial in which one of the participants turned and the other participant wins the trial.

Turn-taking strategy
Number of trials in which the participant does the same thing as the other participant did in the previous trial (not counting both turning, and both crashing). E.g., participant A turns in second 1, and participant B turns in the next trial in second 1. See Fig. S5 for a turntaking strategy example.

Total ICG score
Sum of the points received by the participants throughout the task. Higher total ICG scores mean less dominant behavior across the task (fewer negative feedback points). Crashing corresponds to -10 points.

Difference total ICG score
Difference of the final score of both participants within a pair, in which crashing corresponds to -10 points.
Difference total ICG score =|Final score A -final score B| with crashes = -10 points Dominance ICG score Sum of the dominant behavior of the participant during the task, in which crashing corresponds to 10 points, winning because the other has turned corresponds to points gained, and turning subtracts points lost. Higher dominance ICG score means more dominant behavior across the task.

Cooperative Tetris Task questions
After each round of the Cooperative Tetris Task, participants provided feedback (see Table S4) to their sibling by selecting between positive, neutral, or negative sentences and displayed on the sibling's screen after selection. Further, questions concerning perception of personal success, responsibility for the performance, shared mental representation with their sibling, leadership, and teamwork preference were asked. At the end of the task, participants answered questions about the likability and difficulty of the task, and their prior experience with the Tetris game. For further description of the questions, see Table S4. Note. These questions/items and response options were originally created for the task. A German version of these questions were used in our study. R = reversed item.  Table S5. Note. These questions/items and response options were originally created for the task. A German version of these questions were used in our study.

Questionnaires
Siblings were also part of the survey for other purposes, but are not further considered here.

Complementary analyses
As an exploratory analysis, we compared DoPL-D scores between groups of relatively older versus younger siblings using a t-test.

Cooperative Tetris Task analyses
Spearman's rank correlation was computed to assess the relationship between the total number of cleared lines and feedback between players. Moreover, in order to study the relationship between leadership role during the game (initiator of the actions) and dominance, bivariate correlates were calculated between the mean number of times the participant initiate the actions with the DoPL-D score, and dominance ICG score.
Spearman's correlation was used to explore the relationship between dominance and the leadership question (corrected significance level α = 0.016). Finally, correlation analyses were performed between the total number of cleared lines and perception of success, shared mental representation, and preference to play as a team (corrected significance level α = 0.016).
As exploratory analyses, between-group comparisons using one-way ANOVAs for the task-related questions about the degree of enjoyment, difficulty, and previous experience with the Tetris game were calculated. Also, performance (number of total cleared lines) was compared between brothers and sisters using a t-test.

Interactive Chicken Game analyses
Furthermore, dominance (DoPL-D and ICG) scores were correlated with the motivation question and strategy questions to explore the relationship between dominance and motivation questions at individual level. Due to the correction for multiple comparisons, the corrected significance level was α = 0.0025. Lastly, an independent-sample t-test was performed to compare the condition outcomes between brother and sister pairs.

Questionnaires Correlations
Supplementary    Note. a More than 20% of cells have an expected count of less than 5 and, therefore, Fisher's exact test should be considered instead 71 . LL = both low in dominance, LH = one low in dominance, and one high in dominance, and HH = both high in dominance. No significant differences were found in any demographic variables between clusters.    Figure S5. Bar charts depicting different representative behaviors during the Interactive Chicken Game task. Feedbacks (negative numbers equal losses, while positive numbers equal gains) received by each participant per trial are plotted. a) Example of a turn-taking strategy of a pair consisting of two individuals with low dominance. b) Example of a hetereogeneous pair including one individual with high dominance (sibling B, represented in orange) and one with low dominance (sibling A, represented in blue) who showed a more subordinate behavior turning more times and letting the other one gain more points. c) Example of both individuals with high dominance being all trials crashes.

Interactive Chicken Game performance
Supplementary

Interactive Chicken Game Correlations
A significant positive correlation was found between dominance ICG scores (see Table   S3 for score description) and the perception of the participant that their sibling behaved aggressively (see Table S5  cooperation was negatively associated with dominance ICG score (r = -0.67, p < 0.0001), and dominance scores (DoPL) (r = -0.34, p = 0.014). Only the negative relationship between Dominance ICG score and submissive and perception of cooperation strategies survived after multiple comparison corrections. The motivation questions and other strategies were not significantly correlated with any dominance score (p > 0.05).
Dominance ICG scores, and dominance scores (DoPL) had a significant positive correlation (r = 0.38, p = 0.006). All these findings serve as exploratory results.

Sex Differences
Supplementary Brother and sister pairs did not significantly differ in success. Consistent with our hypothesis, brothers were more dominant than sisters, as they had more crashes and a higher dominance score, while sisters had only one-turningmore frequently. This is supported by previous literature showing that brothers have more sibling conflicts 1,2 , as well as having more power struggles 3 . However, there is also support for more frequent and intense conflicts between sisters 4 , or absence of differences between brothers and sisters 5,6 . Sisters have a more supportive, affective, similar, and close relationship, in line with previous literature describing sister-sister relationships as more emotionally close than between brothers 7,8 . Given that brother and sister pairs did not significantly differ in their dominance score (DoPL), we interpret that the differences in dominance behavior in the task are more likely due to differences in their sibling relationship.